Galactic disc profiles and a universal angular momentum distribution from statistical physics

TL;DR

This paper demonstrates that the exponential stellar surface-brightness profiles in disc galaxies can be explained by a maximum-entropy distribution of angular momentum resulting from radial migration, linking physics to observed galaxy profiles.

Contribution

It introduces a maximum-entropy angular momentum distribution model that explains the exponential surface-brightness profiles of disc galaxies, connecting statistical physics to galactic structure.

Findings

Maximum-entropy angular momentum distribution explains exponential profiles

Model fits observed surface-brightness profiles of disc galaxies

Galaxies with population gradients are close to maximum-entropy state

Abstract

We show that the stellar surface-brightness profiles in disc galaxies---observed to be approximately exponential---can be explained if radial migration efficiently scrambles the individual stars' angular momenta while conserving the circularity of the orbits and the total mass and angular momentum. In this case the disc's distribution of specific angular momenta $j$ should be near a maximum-entropy state and therefore approximately exponential, $dN\propto\exp(-j/\langle j\rangle)dj$. This distribution translates to a surface-density profile that is generally not an exponential function of radius: $\Sigma(R)\propto\exp[-R/R_e(R)]/(RR_e(R))(1+d\log v_c(R)/d\log R)$, for a rotation curve $v_c(R)$ and $R_e(R)\equiv\langle j\rangle/v_c(R)$. We show that such a profile matches the observed surface-brightness profiles of disc-dominated galaxies as well as the empirical exponential profile. Disc galaxies that exhibit population gradients cannot have fully reached a maximum-entropy state but appear to be close enough that their surface-brightness profiles are well-fit by this idealized model.